Question: Simplify the following expression: $a = \dfrac{-2x^2 - 4x + 48}{x + 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ a =\dfrac{-2(x^2 + 2x - 24)}{x + 6} $ Then we factor the remaining polynomial: $x^2 + {2}x {-24} $ ${6} {-4} = {2}$ ${6} \times {-4} = {-24}$ $ (x + {6}) (x {-4}) $ This gives us a factored expression: $\dfrac{-2(x + {6}) (x {-4})}{x + 6}$ We can divide the numerator and denominator by $(x - 6)$ on condition that $x \neq -6$ Therefore $a = -2(x - 4); x \neq -6$